What is the ruling on organising celebrations for the birthdays of children or for wedding anniversaries?

Answer:

There are no celebrations in Islaam except Friday the weekly ‘Eid, the first day of Shawwal – ’Eidal-Adha. The day of ’Arafah might be called an ‘Eid for those who are at ’Arafah on that day, and the days of Tashreeq, following ’Eidul-Adha.

As for birthday celebrations for a person or his children, or wedding anniversaries or the like, none of them are legislated and they are closer to being innovations than to being allowed.